ELASTIC EXPERIMENTAL ANALYSIS OF COLUMNS WITHSPANDREL AND WING WALLS

著者 "TOKUHIRO Ikuo, KYUTOKU Takuma, SHIOYAShinichi, MATSUDA Junji"

journal orpublication title

鹿児島大学工学部研究報告

volume 25page range 49-58別言語のタイトル "腰壁, たれ壁, そで壁付き柱の弾性実験解析"URL http://hdl.handle.net/10232/12451

ELASTIC EXPERIMENTAL ANALYSIS OF COLUMNS WITHSPANDREL AND WING WALLS

著者 TOKUHIRO Ikuo, KYUTOKU Takuma, SHIOYAShinichi, MATSUDA Junji

journal orpublication title

鹿児島大学工学部研究報告

volume 25page range 49-58別言語のタイトル 腰壁, たれ壁, そで壁付き柱の弾性実験解析URL http://hdl.handle.net/10232/00004667

ELASTIC EXPERIMENTAL ANALYSIS OF COLUMNS WITH

SPANDREL AND WING WALLS

Ikuo TOKUHIRO, Takuma KYUTOKU, Shin'ichi SHIOYA*and Junji MATSUDA*

( Received May 31, 1983)

The spandrel and wing walls in the reinforced concrete structure are of important structuralelements in that they bear the shearing force. Since how to design these walls greatly affectthe safety of the structure, it is necessary to estimate correctly the shearing force ratios of thewalls before we design the structure. However, we haven't so far had a standardized method ofdetermining the shearing force ratios for the spandrel and wing walls. So in many cases the design of the column with walls depends on the designers' own methods. Therefore the structuresare designed at fairly various shearing force ratios. In this report the basic data on the shearing force ratios of the column with walls are obtained by the photo-elastic experiments withthe specimens the columns without walls and with walls of various length and variousthicknesses.

§ 1 . Introduction

Although the spandrel and wing walls in the frame are generally neglected in structureanalyses, it is often pointed out that these walls affect largely toward the rigidity, strength andfracture characteristics of building structures ( rahmen frame ). Presently a number of data onthe column with spandrel walls have been reported1 K2) and have been used for the practicalstructural calculation.

But there are few research reports and many obscure points about the column with wingwalls. For example, it is not comprehended how shearing force ratios for the column withspandrel and wing walls should be determined.

In this paper we present it how to deal with the elastic stiffness of columns with spandreland wing walls, and offer the basic data which can be used in practice for the structural calculations. The basic data are

| ) Shearing force ratios of the column with to without walls,ii ) Shearing force ratios of the wall part to the column part in the column with walls.

The stress analysis in order to obtain the data was made through photo-elastic model, andthe photo-elastic experiments gave fairly good agreement with the past reinforced concrete experimental results.

§ 2 . Specimens and Experiments

The specimen material used in this experiment is the epoxy resin plates and steel plates arefixed to make the upper and lower parts of the specimens stiffen as showen in Fig. 1. The col-

* Kagoshima University, Faculty of Engineering, Graduate Students

50 ja**;¥x*»wft m 25 -t (1983)

umn and walls are butted and jointed, and the corners of opening in the walls have a certain

curvature in order to avoid the fracture due to the effect of stress concentration. The dimen

sions and shapes of specimens are shown in Fig. 1 and Table— 1 .

The specimens were set in the apparatus ( Fig. 2 ) and loaded at the half height ( h/2 ) of

the specimens. Isoclinics in case of two kinds of wall thickness have been shown in Photos. —

2 — 3 and isochromatics have been shown in Photos. —4 — 7 ( b/t=6.0 ) and in photos. — 8

-11 ( b/t=3.0 ).

Table— 1 Size of Specimen

Type I ( hR=hL ) " TypeE (hR=HlL)

No. 1 2 3 4 5 6 7 8 9 10

hR

16 32 48 64 80

16 32 48 64 80

hL 32 48 64 84 100

h

•

k X J

1

OL e^wL* •_£WR-» h0R

I

Fig.1. Dimensinons and Shape of the Specimens(scale unit : mm )

c

SPECIMEN(Epoxy Resin)

LOAD-CELL

Fig. 2 • Test Apparatus

JACK

§ 3 . Photo-Elastic Analysis

The photo-elastic sensitivity a are obtained through the tension tests.Columns (thickness =12 mm) ; a=0.95 mm/kgWalls (thickness =2 mm, 4 mm) ; a=0.93 mm/kg

There are shown the isochromatics and bending moment diagram of columns without wall in

Elastic Experimental Analysis of Columns with Spandrel and Wing Walls 51

Photo. —1 and Fig. 3 respectively, in which bending moment values are obtained from eq. (1).

ab " 6a (1)

^ _ M(top)+ M(bottom)Q~ h (10

where M '. bending moment

n '. fringe order

Q ! shearing force

a I photo-elastic sensitivity of the column

D ! column depth

b I column thickness

bD2Z= c \ section modulus of the columnsb

h '. height of column

The difference between the stress of the left and right columns is so little as to be neglec

ted.

The shearing unit stresses xXy in the wall are obtained as follows \

TXy=

where

txv=—2— sm2^ (2)

Ox , <72 \ principal stresses

a \ photo-elastic sensitivity of the wall

t \ wall thickness

S \ angle of principal stress direction to datum line

The principal stress difference ( <j\ —<r2) is obtained from the isochromatics, and the angle0 is 45 digrees on the middle horizontal section as shown in Photos. —2 and 3 , and therefore

sin 20 in eq. (2) is equal to 1.0 .

The shearing forces on the middle height section of the wall are obtained by integrating the

shearing unit stress xXy as follows.re*L rUx. n

QmL=t/ TXydx=J ~2a~dxr^wB re** n

QwR=tjfo zXydx=Jo -^dx(3)

where QWL , QWR '. shearing force on the lefthand-side wall section and that on the right-hand-side wall section

where ^WL , ^WR : length of the lefthand-side wall and that of the righthand-side wall

The stresses ( fringe orders ) on the column with the wall are very complicated, according

ly the shearing forcese ( Qc ) of the column with the wall were determined following equation

(4).

Qc=Q-(Qo+Qw) (4)where Q I total load subjected to specimen

*• AG it1 tb ±¥ 13* SPW 5S 25 ^r (1983)

Q0 : shearing force of the column without wall

Qw = Qwl+ Qwr • shearing force on the middle height section of the wall

Photo.— 1 Isochromatics of Columns without Wal

Fig. 4 • Fringe Orders

Specimen |=3.0 ^ =0.64 ^!=0.48

^=1.53 4r=2.185

Photo.— 2 Isoclinics

D „ n floL iloRT=6.0, -T—= -7—t h h

gwt. gwLD ~ D

Y///////(//(///////////////////A:•:;

12S>\BHmm

Q=12jOOI:3'

5£f̂ =094

|l2795ty-*«

5.621*5.6c•

/

f

287.2/ U;i 28 2.5 J;!;

Y/////A V////////////7/7///////A

Fig. 3. Bending Moment Diagram in the Columnswithout Wall of Photo 1 .

-o —

V

Fig. 5 • Typical Shearing unit Stresses Distribution

on the middle Height Section of the Wing

Wall

Photo.— 3 Isoclinics

=̂45" ^=3.0 ^=^=0.48 ^=^=2.185

Pho

to.—

4Is

ochr

omat

ics

(dar

kfi

eld

)

bho

iho

R2w

T=

6.0

-^

=0.

48^

=0

.32

^2

.18

5in

=2

.85

0

Ph

oto

.-6

b-

.h0

t"=

6.0

Isoc

hrom

atic

s(

dark

fiel

d)

—=

0.48

-p-=

1.53

-g-

=0

.64

=2

.18

5

Phot

o.—

5Is

ochr

omat

ics

(dar

kfi

eld

)

hoL

HOB

^WL

^Wx=

ir=

()-4

8tt

=^

^=6.0

2.1

85

Phot

o.—

7Is

ochr

omat

ics

(da

rkfi

eld

)

b=6.Q

^=^=

0.80

£-*

•=0

.87

5

W m o o

Phot

o.—

8Is

och

rom

atic

s(

dar

kfi

eld

)

1>=3.0

~=0.4

8^=

0.32

4r=2.1

85^i=

2-85

Phot

o.—

10Is

ochr

omat

ics

(da

rkfi

eld

)

=3.0

^Q

.64

=0

.48

IT

=1.5

3=2

.18

5

Phot

o.—

9Is

ochr

omat

ics

(da

rkfi

eld

)

—=

—=

0.48

-p-=

T^=

3.02

.18

5

Ph

oto

b t3

.0

•11

Isoc

hrom

atic

s(d

ark

fiel

d)

hoL

_hO

R_

^»L

<?WR

h"

h-°

-80

~D~—

W=

0.8

75

c5

» X % H 4* 2§ SS OrT

as

OS

en

Elastic Experimental Analysis of Columns with Spandrel and Wing Walls 55

§ 4 . Experimental Results

. The shearing force ratio Qw/(Qc+Qw) of the wing walls to column with wall plus wingwalls is presented in Fig. 7 and increases almost linearly to ^W/D=4.0

The empirical equations are

for b/t=3.0 ,

0^=0.13(^)^0.13for b/t=6.0

where, 0.5^^<4.5The shearing force ratio Qc/Qo of the column with to without walls is presented in Fig. 8

and increases almost linearly to ^W/D=2.5

The emprical equations are

for b/t=3.0

!-1.9o(£)+0.70for b/t=6.0

£=1.65(£)+0.78where,

Although the plates over ^W/D>2.5 are somewhat scattered, it is assumed that Qc/Qo isconstant.

0.5^-^2.5

,06

Qo *W —*WL *" 2WR

L Q=Qo+Qw+QcQW = QWL+QWR

Fig. 6 • Shearing Forces of Column without Wall,

with Wall, and Wall Sign of Shape

(5a)

(5b)

(6a)

(6b)

CUQc

Fig. 7. Shearing Force Ratios of Wing Walls to

Column with Walls plus Wing Walls along both Sides.

56 !SA*;*I**Bf§ft«S H 25 ^ (1983)

1 0

• £=3.0

8

O £=6X)

i

•

6 I^"

/J•

4

(

*~ o o J

4 y /O

/2

i>/

C) 2 3 4 i > € r 6

-*

Fig. 8. Shearing Force Ratios of Column with Walls to without Wall.

LOT

Fig. 9 • Each Shearing Force Ratio, a Column with or without Walls

to Total Shearing Force.

Elastic Experimental Analysis of Columns with Spandrel and Wing Walls 57

§5. Comparison of the Experimental Results through the Epoxy Resin Model with those throughthe Reinforced Concrete Model

According to the data presented in § 4, the experimental results through the epoxy resinmodel were compared with those through the reinforced concrete model.

The dimensions of the specimen compared are shown in Fig. 10The two reinforced concrete specimens of the same dimensions were tested by Drs. Y.

Higashi and M. Ohkubo3). One specimen was monotonically loaded, and the other was cyclically loaded. The shearing forces were obtained through the measure by strain gauges.

The shearing force ratio of the column with to without wing walls was obtained from Fig.8 and that of the column with only spandrel wall was obtained by using next equation in ref-

ference (2).

i=e—(^+1,(7)

The comparisons of the reinforced concrete experiments with the epoxy model experimentsare shown in Table. — 2 .

§ 6 . Considerations and Conclusions

In comparisons in § 5, these degree of errors are practically permissible considering folio-wings,

| ) As both specimens are quite small, the measured values are not always accurate ex

tremely

H) The walls of the compared reinforced concrete specimen is eccentric?.

The data, which are obtained from this experiment, may be applied to the actual structure

calcurations.

H ^r20

Fig.10. the Specimen (b / t =4.0) of Experiment by Higashi and Ohkubo3)

58 «»A*¥i¥*Br» m 25 3% (1983)

Table- 2 Comparison of Experimental Values by Authors with those by Higashiand Ohkubo3)

Opening Ratio h0/( D+ l« ) 2 1 2/3

Wall Length Ratio ^W/D 1 0 2

Shearing Force Ratio (Q)

Reinforced Concrete (1)

Experiment (2)

0.28

0.31

0.17

0.14

0.55

0.55

Epoxy Model Experiment 0.26 0.17 0.57

(1) monotonic increasing load

(2) cyclic increasing load

Reference

1) Ikuo Tokuhiro and Akio

Sasaki "Studies on Elastic Rigidity of

Columns with Spandrel Walls ( I ) "

Transactions of Architectural Institute of

Japan, No. 304 Jun. 1981

2) Ikuo Tokuhiro and Takuma Kyutoku

" Studies on Elastic Rigidity of Col

umns with Spandrel Walls ( H ) Trans

actions of the Architectural Institute of

Japan, No. 318, Aug. 1982

3) Masamichi Ohkubo, Hiroaki Eto and

4)

Youichi Higashi " Cracks and Statical

Hysterisis-Loops of Reinforced Concrete

Frames with Spandrel Walls Cast Simul

taneously " Transactions of the

Architectural Institute of Japan No. 169,Feb. 1971

Masamichi Ohkubo " studies on Rigidities, Strength and Hysteretic Character

istics of Reinforced Concrete Frames

with Spandrel or Wing Walls " Transac

tion of the Architectural Institute of

Japan, No. 186, Aug. 1972